Principles of Pure Mathematics - 2025 entry
| MODULE TITLE | Principles of Pure Mathematics | CREDIT VALUE | 30 |
|---|---|---|---|
| MODULE CODE | MTH0001 | MODULE CONVENER | Dr Jamie Walker (Coordinator) |
| DURATION: TERM | 1 | 2 | 3 |
|---|---|---|---|
| DURATION: WEEKS | 11 | 11 | 0 |
| Number of Students Taking Module (anticipated) | 30 |
|---|
DESCRIPTION - summary of the module content
This module develops core mathematical skills essential for progression into a degree in mathematics or other quantitative disciplines. It lays the foundation of Algebra, Trigonometry, Calculus and complex numbers for more advanced mathematical studies by bringing you to a level of knowledge and competence equivalent to the pre-requisite for a first year mathematics at any quantitative degree programme. In this module you will get a grasp of Algebra, which is the study of symbolic representations and the rules for manipulating symbols such as the skills required in ‘backwards thinking’. You will develop competency to confidently manipulate algebraic expressions, to solve equations and inequalities, as well as to explore functional relationships. Calculus is another part of mathematics to cover in this module, which is concerned with the study of continuous changes, and has two branches, differential calculus (the study of measuring rates of change) and integral calculus (the study of accumulation of quantities), which are precisely linked by the Fundamental Theorem of Calculus. You will also learn about Trigonometry and complex numbers. Those skills are fundamental tools for the study of mathematics across the physical, engineering, life and environmental sciences. In this module you will also learn how to: use theories, definitions and properties; analyse mathematical statements; use logic and critical thinking to perform mathematics; present findings and communicate results in a coherent way.
On successful completion of this module you will be equipped with the skills to apply those mathematical concepts in different contexts, and you will have a sound understanding of fundamental mathematical techniques necessary to handle a diverse range of problems in mathematics, engineering and sciences.
AIMS - intentions of the module
This module aims to enhance your ability to think logically, to manipulate and analyse complex relationships, to question given assumptions as well as to recognise the simple ideas underpinning a given problem. It is developed to renew the background knowledge which you have been in contact within schools, and to advance your experience with doing mathematics in a more rigorous way.
INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)
Module Specific Skills and Knowledge:
1. Manipulate algebraic and numerical expressions accurately and with confidence
2. Recognise and solve equations involving logarithmic, exponential, trigonometric and hyperbolic functions
3. Sketch the graphs of a variety of functions of one variable
4. Perform accurate calculus manipulations using a variety of standard techniques
5. Understand, manipulate and analyse expressions involving complex numbers
Discipline Specific Skills and Knowledge:
6. Manipulate basic mathematical objects necessary in order to progress to successful studies in mathematics, engineering and sciences
7. Communicate mathematics effectively and clearly
8. Demonstrate an ability to model a given problem mathematically, i.e. to find the mathematical formula which represents the problem
Personal and Key Transferable/ Employment Skills and Knowledge:
9. Formulate and solve problems and communicate reasoning and solutions effectively in writing
10. Use learning resources appropriately
11. Communicate ideas and plans in a clear and concise way
12. Exhibit self-management and time management skills
SYLLABUS PLAN - summary of the structure and academic content of the module
- Basic algebra: indices; algebraic expressions; arithmetic operations: addition, subtraction, multiplication; division of algebraic expressions; factor and remainder theorem
- Equations and inequalities: solving linear equations; solving quadratic equations using: factorisation, discriminant method or completed square form; solving linear and quadratic inequalities
- Functions: dependent and independent variables; domain and range; Real functions: sums, differences, product, quotient and function composition; inverse function; continuity of functions
- Elementary functions and graphs including polynomials, exponential, logarithm and natural logarithm
- Trigonometric functions and identities including solving equations
- Complex Numbers: Cartesian and polar coordinates, Argand Diagram, arithmetic operations, De Moivre’s theorem
- Basic Differential Calculus (one variable): definition of the derivative; derivatives of standard functions
- Differentiation techniques: chain, product and quotient rules; implicit differentiation
- Application of differentiation: maxima and minima of functions with curve sketching; Mean Value Theorem; tangent and normal lines to a curve; Taylor series
- Basic Integral Calculus: definition of the integral as a limit of a sum and graphical principles of integration; Fundamental Theorem of Calculus; definite and indefinite integrals; integration of standard functions
- Integration methods: Integration by substitution, integration using partial fractions, integration by parts
- Applications of integration: areas under curves or between two curves; volumes of solid of revolution; numerical integration using Taylor series
LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
| Scheduled Learning & Teaching Activities | 88 | Guided Independent Study | 212 | Placement / Study Abroad | 0 |
|---|
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
| Category | Hours of study time | Description |
| Scheduled learning and teaching activities | 88 | Lectures and tutorials |
| Guided independent study | 212 | Guided independent study |
ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
| Form of Assessment | Size of Assessment (e.g. duration/length) | ILOs Assessed | Feedback Method |
|---|---|---|---|
| Weekly exercises (term 1) | 10 x 1 hour | 1-12 | Exercises discussed in class, solutions provided |
| Weekly exercises (term 2) | 10 x 1 hour | 1-12 | Exercises discussed in class, solutions provided |
SUMMATIVE ASSESSMENT (% of credit)
| Coursework | 20 | Written Exams | 80 | Practical Exams | 0 |
|---|
DETAILS OF SUMMATIVE ASSESSMENT
| Form of Assessment | % of Credit | Size of Assessment (e.g. duration/length) | ILOs Assessed | Feedback Method |
|---|---|---|---|---|
| 2 Online quizzes | 10 | 2 x 1 hour + 30 mins | 1-12 | Electronic |
| Test 1 | 10 | 1 hour | 1-12 | Annotated scripts |
| Written exam A | 30 | 2 hours | 1-12 | Annotated script |
| 2 Online quizzes | 10 | 2 x 1 hour + 30 mins | 1-12 | Electronic |
| Test 2 | 10 | 1 hour | 1-12 | Annotated scripts |
| Written exam B | 30 | 2 hours | 1-12 | Annotated script |
DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
| Original Form of Assessment | Form of Re-assessment | ILOs Re-assessed | Time Scale for Re-assessment |
|---|---|---|---|
| 2 Online quizzes | 2 Online quizzes (2 x 5%) | 1-12 | Referral/deferral period |
| Test 1 | Test 1 (10%) | 1-12 | Referral/deferral period |
| Written exam A | Written exam A (30%) | 1-12 | Referral/deferral period |
| 2 Online quizzes | 2 Online quizzes (2 x 5%) | 1-12 | Referral/deferral period |
| Test 2 | Test 2 (10%) | 1-12 | Referral/deferral period |
| Written exam B | Written exam B (30%) | 1-12 | Referral/deferral period |
RE-ASSESSMENT NOTES
Deferral – if you have been deferred for any assessment, you will be expected to complete relevant deferred assessments as determined by the Mitigation Committee. The mark given for re-assessment taken as a result of deferral will not be capped and will be treated as it would be if it were your first attempt at the assessment.
Referral – Reassessment will be by a written exam (worth 50% of the module mark) for each term where the mark for the term is less than 40%. The mark given for a re-assessment taken as a result of referral will be capped at 40%.
RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener
information that you are expected to consult. Further guidance will be provided by the Module Convener
Basic reading/Web-based and electronic resources:
• ELE
Other resources:
• McGregor, C. M. 2010, Fundamentals of University Mathematics, 3rd ed., Oxford: Woodhead.
• Hass, J. 2020, Thomas' calculus, Pearson.
Reading list for this module:
| CREDIT VALUE | 30 | ECTS VALUE | 15 |
|---|---|---|---|
| PRE-REQUISITE MODULES | None |
|---|---|
| CO-REQUISITE MODULES | None |
| NQF LEVEL (FHEQ) | AVAILABLE AS DISTANCE LEARNING | No | |
|---|---|---|---|
| ORIGIN DATE | Thursday 29th July 2021 | LAST REVISION DATE | Friday 13th September 2024 |
| KEY WORDS SEARCH | Algebra, Trigonometry, Functions, Calculus, Complex Numbers |
|---|
Please note that all modules are subject to change, please get in touch if you have any questions about this module.
